O'Reilly logo

Topics in Matrix Analysis by Charles R. Johnson, Roger A. Horn

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 5

The Hadamard product

5.0    Introduction

In this chapter, we study a matrix product that is much simpler than the conventional product, but is much less widely understood. It arises naturally in a variety of ways and enjoys considerable rich structure.

5.0.1    Definition. The Hadamard product of A = [aij] ϵ Mm,n and B = [bij] ϵ Mm,n is defined by AB ≡ [aijbij] ϵ Mm,n.

    The conformability condition for the Hadamard product is simply that both matrices have the same dimensions, and the multiplication is carried out entry by entry, as in conventional matrix addition. Simply imagine the superposition of one array upon the other with a single scalar multiplication performed in each cell.

5.0.2    Example. If

then

    The Hadamard ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required